CERTIFICATION FILED AS EXHIBIT 13(B) TO FORM N-CSR

Name of Issuer:         AMG FUNDS III – AMG GW&K INTERNATIONAL SMALL CAP FUND

In connection with the Report on Form N-CSR of the above-named issuer that is accompanied by this certification, the undersigned hereby certifies, to her knowledge, that:

1. The Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

2. The information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the issuer.

Dated: August 3, 2023

/s/ Keitha L. Kinne

Keitha L. Kinne

Principal Executive Officer

CERTIFICATION FILED AS EXHIBIT 13(B) TO FORM N-CSR

Name of Issuer:         AMG FUNDS III – AMG GW&K INTERNATIONAL SMALL CAP FUND

In connection with the Report on Form N-CSR of the above-named issuer that is accompanied by this certification, the undersigned hereby certifies, to his knowledge, that:

1. The Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

2. The information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the issuer.

Dated: August 3, 2023

/s/ Thomas Disbrow

Thomas Disbrow

Principal Financial Officer